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Appendix | |

1 It is completely common to plot thby multiplying each by 100.2 If one knows any two values; the thsum from 1 (or 100). That’s how allcan be represented by plotting a poitwo dimensions.

The Teas Graph

ese fractional solubility parameters

ird is known by subtraction of theirthree types of solubility parametersnt on a graph which exists only in

A. FRACTIONAL SOLUBILITYPARAMETERS (THE TEAS GRAPH)

Decades ago, before software for personal computers madeit possible (and even easy) to draw graphs or plots of three-dimensional solubility parameters, the Teas Graph(Diagram or Chart) was commonly used, with goodreason. It is less useful today.

The Teas Graph allows one to represent the threedimensions or scales (disperse, polar, hydrogen bonding)of solubility in a “flat” two-dimensional plot. It enablessolvents (or solvents and soils) to be positioned relative toeach other in three directions.

All three were clearly visible; they were the three axes ona triangular plot.

Essentially, the axes of Jean Teas’ GraphA,B were anoverlay of the three solubility scales.

An unpopulated example of a Teas Graph is shown inFigure C12-1.

� The three axes are the same length, so their intersectingangles are those of an equilateral triangled60 degrees.

� The axes are connected “head to tail.” That means ateach corner of the triangle, the intersecting axes havethe values 1.00 and 0.00.

� Positioned at the lower left corner of Figure C12-1would be those solvents for which hydrogen bondingintermolecular force is the dominant characteristic. Atthe top and right corners would be those which aredominated by polar and disperse intermolecular forces,respectively.

� For clarity in Figure C12-1, the three solubility scales areprinted in different colors.

B. HOW TO USE THE TEAS GRAPH

What’s plotted in a Teas Graph are not solubility parame-ters per se, but three “fractional solubility parameters.”

These are defined by Equations C12-1 A, C12-B, andC12-C as fD, fP, and fH, which each have a value betweenzero and unity1.

fD ¼ ddisperse

fddisperse þ dpolar þ dH bondinggC12�1A

fP ¼ dpolar

fddisperse þ dpolar þ dH bondinggC12�1B

fH ¼ dH bonding

fddisperse þ dpolar þ dH bondinggC12�1C

Each is a fraction of the algebraic sum of all three numericalsolubility parameters, in any consistent system of units.Naturally, the sum of the three is the dimensionless value,unity2.

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Figure C12-1

3 An excellent example of a fully populated Teas Graph is Figure 10 ofthe resource which can be found at http://206.180.235.133/sg/bpg/annual/v03/bp03-04.html.

Appendix C12 The Teas Graph

� Note carefully, this algebraic sum is NOT the TOTAL orHildebrand Solubility Parameter, which is given byEquation 2.7.

One cannot multiply a fractional solubility parameter bythe known value of the Hildebrand Solubility Parameterand obtain any credible answer.

In a Teas Graph it is useful is to notice generally thatdifferent solvent classes and soil types have differentamounts of the three intermolecular forces.

For example:

� All hydrocarbons will always be found at the lowerright-hand corner.

� Neither the lower left-hand or top corners will ever bepopulated, as the former would represent solventsdevoid of disperse intermolecular forcedthat which isnormally found in the largest amount; and the latterwould represent solvents whose structure was totallybased on centers of polarity and devoid of any otherstructural elements such as those to which the center ofpolarity could be attached.

� Nearly all solvents, polymers, and soils will be locatednear the lower-right center of the Teas Graph, or in itslower right-hand corner.

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� A few general types of solvents are noted in the TeasGraph of Figure C12-23.

A Teas Graph can be used with any single system of solu-bility parametersdHansen, Hoy, van Krevelen, and others.

C. A LIMITATION OF THE TEASGRAPH

A Teas Graph is a representation without numericalmeaning. Actual measured or calculated values of anysolubility parameters are not plotted and cannot bededuced from any Teas Graph. The plotted coordinatesmight be, for example, 0.90, 0.04, 0.06 (totaling unity) fordisperse, polar, and hydrogen bonding, yet one wouldn’tknow of what numerical value these coordinates werea fraction.

A Teas Graph is:

� A valid attempt to visually describe solubilityrelationships.

Figure C12-3

Figure C12-2

The Teas Graph C12 Appendix

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Appendix C12 The Teas Graph

� Not a representation of the absolute values of solubilityparameters.

One can’t calculate a specific solubility distance, such as RA,between two materials using just the fractional solubilityparameter information found in a Teas Graph. This isbecause one doesn’t know the numerical value of anysolubility parameter in MPa1/2, or in any other unit system.

Fractional solubility parameters are relative information,not absolute information.

D. A CRUCIAL FLAW OF THE TEASGRAPH

Unfortunately, a Teas Graph is based on a demonstrablyfalse4 assumptiondthat the Hildebrand SolubilityParameters for all plotted materials are the same.

This flaw is clearly demonstrated in Figure C12-3. This isa plot of separation in solubility parameters, as representedin both relative (fractional) and absolute (HildebrandSolubility Parameter) terms.

4 Chapter 2.7.2 provides examples of the inverse of this flaw: Thatknowledge of the Hildebrand Solubility Parameter provides knowledgeabout the solvent structuredwhich it doesn’t.

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Yes, there is some relationship5 between the numericalspacing among solvent pairs in a Teas Graph, and RA fromEquation 2.8.

Seeking a separation distance on a Teas Graph equivalentto an RA value of 8 MPa1/2 (Chapter 3.28), one finds inFigure C12-3 that the corresponding fractional value couldbe from 0 to 0.4, and might be around 0.25. The reason forthis spread in results in Figure C12-3 is that the basicassumption behind the Teas Graph is untenabledtheHildebrand solubility parameters of all plotted materialsare not the same.

This author doesn’t recommend use of the TeasGraph6, and instead prefers calculations of two-dimen-sional RA plots (imperfect as they are) such as those inFigure 2.37.

Endnotes

A. Teas JP. Graphic Analysis of Resin Solubilities. Journal of PaintTechnology. 1968;40(516):19e25.

B. Teas, Jean P. Predicting Resin Solubilities. Columbus, Ohio: AshlandChemical Technical Bulletin, Number 1206.

5 The blue line in Figure C12-3 is a linear fit of about 2100 data points.Each point is based on a pair of cleaning solvents chosen froma database of more than 200 chemicals. The pair of solvents is firstplotted on a Teas Graph, and the linear two-dimensional separationdistance (Delta R) between them is calculated. Then the RA betweenthem is calculated using Equation 2.8 and their known values of HSP.The correlation coefficient for the large number of data points is only0.55, representing no correlation at all.6 For those interested, there is a DOS-based computer programdeveloped at Stanford University to aid in the selection of solvents usingthe Teas Graph. It is known as “Teas Time” and can be downloaded forfree from http://cool.conservation-us.org/packages/.